In view of the complex constraints and huge solution space in the mission scheduling process of agile Earth observation satellite, this study innovatively proposes an improved high-order quantum genetic method to solve this problem. The paper first comprehensively considers the time-dependent characteristics, attitude maneuverability, energy consumption and storage constraints of agile earth observation satellites, and establishes a satellite scheduling model that integrates multiple constraints. Secondly, inspired by the higher-order quantum genetic algorithm, a higher-order quantum genetic method based on the adaptive mutation transfer strategy is proposed. The quantum registers operator and adaptive mutation transfer operation ensure that the algorithm achieves global optimization while achieving computational efficiency. Finally, this paper demonstrates through computational experiments that the proposed method has high computational efficiency in the large-scale satellite missions scheduling process, and effectively avoids the problem that traditional higher-order quantum genetic algorithms easily fall into local optimality. This method can be considered for application in the engineering practice of agile Earth observation satellite scheduling based on large-scale missions.